In this work we study the relativistic mechanics of continuous media on a
fundamental level using a manifestly covariant proper time procedure. We
formulate equations of motion and continuity (and constitutive equations) that
are the starting point for any calculations regarding continuous media. In the
force free limit, the standard relativistic equations are regained, so that
these equations can be regarded as a generalization of the standard procedure.
In the case of an inviscid fluid we derive an analogue of the Bernoulli
equations. For irrotational flow we prove that the velocity field can be
derived from a potential. If, in addition, the fluid is incompressible, the
potential must obey the d'Alembert equation, and thus the problem is reduced to
solving the d'Alembert equation with specific boundary conditions (in both
space and time). The solutions indicate the existence of light velocity sound
waves in an incompressible fluid (a result known from previous literature
[19]). Relaxing the constraints and allowing the fluid to become linearly
compressible, one can derive a wave equation from which the sound velosity can
again be computed. For a stationary background flow, it has been demonstrated
that the sound velocity attains its corrrect values for the incompressible and
non-relatvistic limits. Finally, viscosity is introduced, bulk and shear
viscosity constants are defined, and we formulate equations for the motion of a
viscous fluid.Comment: Latex, 44 pages, 5 figure
